Ok they use 'mate-session' and not the new 'gnome-session' (or a fork of the gnome-session from Gnome 3).
If Mate is a fork of Gnome2, you've to use the 'old' solution to launch this cairo-dock session: simply launch your (Mate) session as usual but do not launch the (mate-)panel at startup (or hide it) => Remove the last Gnome Panel
(I guess you've to use mateconf-editor
instead of gconf-editor
PS: don't forget to launch Cairo-Dock at startup
(right click on the dock / Cairo-Dock / Launch at startup)
You can also load the default panel theme for this Cairo-Dock session: right click on the dock / Cairo-Dock / Theme / Default-Panel / Apply)